Yes, I read the entire adventure 1st. (in fact I'll often read it through several times...)
1) That way I know if there's things I need to adjust for some reason.
2) I'll know the NPCs well enough to not really need their stat blocks.
3) I'll know if there's any additional prep I'd like to do - map making, 3d parts, ordering specific minis, painting specific minis....
The earlier I know these things, the better.
And in the case of PF adventure paths? Each issue is usually written by a different author. And very often later volumes have important plot/NPC developments that would be really nice to know of early on. But aren't possible due to that different author set-up. I don't want to know about, or mind, this stuff as a player. But as a DM? Kinda important. Refer back to my 1-3 list.
So I NEVER run a PF AP before I have all 6 volumes.